Mr Johnson announced last week that he wanted to give local councils the power to require new faith schools to accept up to a quarter of pupils from other faiths or none.

But he said a voluntary deal had now been reached with both the Catholic Church and the Church of England, meaning his proposed new laws were no longer necessary.

Mr Johnson said: "I have listened carefully to colleagues on this issue and recognise that we all share the same goal for a more cohesive society where faith schools play an important part in building understanding and tolerance of other faiths and communities."

Mr Johnson last week announced he was planning to introduce laws to force faith schools to act with an amendment to the Education and Inspection Bill.

The amendment would have enabled councils to require new faith schools to select up to 25 per cent of their intake from pupils of other faith backgrounds or those with no religious beliefs.

But last night Mr Johnson said such legislation would not be appropriate, though school inspectors would get new powers to make sure faith schools promoted community cohesion.

The plans announced last week provoked a storm of protest from conservative commentators and Catholics.

The Catholic Archbishop of Birmingham, the Most Reverend Vincent Nichols, described Mr Johnson’s proposed amendment as "ill-thought-out, unworkable, contradictory of empirical evidence and deeply insulting".

The pair met for talks and the Archbishop, who chairs the Catholic Education Service, welcomed the agreement which had been reached.

He said: "I welcome the decision by the Secretary of State for Education and Skills not to table an amendment to the Education and Inspection Bill concerning the planning of future faith schools.

"I am grateful to Alan Johnson for the attention he and his colleagues gave to the concerns of the Catholic community and for the discussions I held with him yesterday.

"In those discussions we came to a broad agreement about how future Catholic schools could be planned in ways that ensure that they always meet the needs of Catholic parents. This is of prime importance to Catholics."

He thanked the "very many" Catholics who had written to their MPs to protest.

Canon John Hall, the Church of England’s chief education officer, also welcomed the deal.

"The Government have promised all along to listen to the views of faith groups in this process, and this latest announcement is a result of their having done so," he said.